Problem: The value of $\sqrt{63}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Solution: Consider the perfect squares near $63$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $49$ is the nearest perfect square less than $63$ $64$ is the nearest perfect square more than $63$ So, we know $49 < 63 < 64$ So, $\sqrt{49} < \sqrt{63} < \sqrt{64}$ So $\sqrt{63}$ is between $7$ and $8$.